How to Solve Polynomial Equations Using Quadratic Form Substitution

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on solving polynomial equations that appear in "quadratic form" using the substitution method (often called u-substitution, though the narrator uses 'a'). The video begins by defining what makes an equation "quadratic form"—specifically when the exponent of the leading term is double the exponent of the middle term. Through six distinct examples, the narrator demonstrates how to temporarily replace complex variable expressions with a single variable to simplify the equation into a standard quadratic that can be factored.